Luís Daniel Abreu, Afonso S. Bandeira
We will prove an analogue of Landau's necessary conditions [Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967).] for spaces of functions whose Hankel transform is supported in a measurable subset S of the positive semi-axis. As a special case, necessary density conditions for the existence of Fourier-Bessel frames are obtained.
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Multivariate Bessel functions and multivariate Hankel transforms
本文将贝塞尔函数推广到多维，并相应地将汉克尔变换在微分下的性质推广到多维情形。
Uniform weighted inequalities for the Hankel transform transplantation operator
该研究建立 Hankel 变换移植算子的一致加权及加权向量值不等式，并据此推广 Rubio de Francia 的迁移定理。
In this article we study the fractional Hankel transform and its inverse on certain Gel'fand-Shilov spaces of type S. The continuous fractional wavelet transform is defined involving the fractional Hankel transform. The continuity of fractional Hankel wavelet transform is discussed on Gel'fand-Shilov spaces of type S. This article goes further to discuss the continuity property of fractional Hankel transform and fractional Hankel wavelet transform on the ultradifferentiable function spaces.
Hankel Multipliers of Laplace Transform Type
本文证明了 $(0,1)^n$ 上 Laplace 变换类型的 Hankel 乘子具有弱型 (1,1) 性质，并分析了 Bessel 算子虚幂的 Lp 有界性。
We deal with a class of one-parameter family of integral transforms of Bargmann type arising as dual transforms of fractional Hankel transform. Their ranges are identified to be special subspaces of the weighted hyperholomorphic left Hilbert spaces, generalizing the slice Bergman space of the second kind. Their reproducing kernel is given by closed expression involving the $\star$-regularization of Gauss hypergeometric function. We also discuss their basic properties such as their boundedness and we determinate their singular values. Moreover, we describe their compactness and membership in $p…
In this paper, we extend the concept of continuous Bessel wavelet transform in $L^p$-space and derived the Parseval's as well as the inversion formulas. By using Bessel wavelet coefficients we characterized the Besov- Hankel space.
Abelian and Tauberian Results for the Fractional Hankel Transform of Generalized Functions
本文通过分数阶 Hankel 变换研究分布的拟渐近行为，提出了连接 Zemanian 空间中广义函数渐近性与其变换渐近性的 Tauber 型结果，并建立了分布分数阶 Hankel 变换的初值与终值定理。
Pseudo-differential operators associated with the fractional Hankel-Bessel transform
本文提出了一种基于分数Hankel-贝塞尔变换的伪微分算子理论，通过引入分数傅里叶型相位，构建了新的符号类并研究了其在加权L^p空间和分数Sobolev空间上的有界性。
In this article we study the Poisson summation for Hankel transform in the sense of Braverman-Kazhdan-Ngo in the special case of $L$-embedding $ρ: GL_1\rightarrow GL_2$. We view such a summation formula as the generalization of the classical Voronoi summation formula.
Asymptotic estimates for the growth of deformed Hankel transform by modulus of continuity
本文推导了变形Hankel-Lipschitz空间上变形Hankel变换范数增长的渐近估计，并给出了Dunkl-Lipschitz空间中Dunkl变换有界性的必要条件，改进了该情形下的Hausdorff-Young不等式。
Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators
本文研究Ehrenpreis-Hörmander意义下卷积算子的满射性，通过有限Hankel变换的渐近展开给出径向函数可逆的充分条件，并提出处理非原点奇点的新方法。
Abelian and Tauberian results for the fractional Hankel transform in Zemanian-type spaces
本文在Zemanian广义函数空间中给出分数阶汉克尔变换的阿贝尔型定理，构造新Zemanian型空间并证明其对偶空间为已知允许FrHT的最大分布空间，进而建立FrHT的新阿贝尔和陶伯型结果。
Let H(f)(x)=\int_{(0,infty)^d} f(v) E_{x}(v) dν(v), be the multivariable Hankel transform, where E_{x}(v)=\prod_{k=1}^d (x_k v_k)^{-a_k+1/2} J_{a_k-1/2}(x_k v_k), dν(v)=v^a dv, a=(a_1,...,a_d). We give sufficient conditions on a bounded continuous function m(v) which guarantee that the operator H(m Hf) is bounded on L^p(dν) and of weak-type (1,1), or bounded on the Hardy space H^1((0,infty)^d, dν) in the sense of Coifman-Weiss.
Abelian and Tauberian results for the fractional Hankel transform in Zemanian-type spaces
本文在Zemanian广义函数空间及新构造的Zemanian型空间（其对偶为已知允许FrHT的最大分布空间）中，建立分数阶汉克尔变换的阿贝尔型和陶伯型结果。
We show that all Hankel operators $H$ realized as integral operators with kernels $h(t+s)$ in $L^2 ({\Bbb R}_{+}) $ can be quasi-diagonalized as $H= {\sf L}^* Σ{\sf L} $. Here ${\sf L}$ is the Laplace transform, $Σ$ is the operator of multiplication by a function (distribution) $σ(λ)$, $λ\in {\Bbb R}$. We find a scale of spaces of test functions where ${\sf L} $ acts as an isomorphism. Then ${\sf L}^*$ is an isomorphism of the corresponding spaces of distributions. We show that $h= {\sf L}^* σ$ which yields a one-to-one correspondence between kernels $h(t)$ and sigma-functions $σ(λ)$ of Hankel…
For a fixed reals $c>0$, $a>0$ and $α>-\frac{1}{2}$, the circular prolate spheroidal wave functions (CPSWFs) or 2d-Slepian functions as some authors call it, are the eigenfunctions of the finite Hankel transform operator, denoted by $\mathcal{H}_c^α$, which is the integral operator defined on $L^2(0,1)$ with kernel $H_c^α(x,y)=\sqrt{cxy}J_α(cxy)$. Also, they are the eigenfunctions of the positive, self-adjoint compact integral operator $\mathcal{Q}_c^α=c\mathcal{H}_c^α\mathcal{H}_c^α.$ The CPSWFs play a central role in many applications such as the analysis of 2d-radial signals. Moreover, a re…
SG-Hankel Pseudo-Differential Operators on Weighted Gelfand-Shilov Type Spaces and a Numerical Example
本文研究了SG-Hankel伪微分算符在加权Gelfand-Shilov型空间上的性质，并通过数值例子验证了理论预测的空间衰减。
We classify all functions which, when applied term by term, leave invariant the sequences of moments of positive measures on the real line. Rather unexpectedly, these functions are built of absolutely monotonic components, or reflections of them, with possible discontinuities at the endpoints. Even more surprising is the fact that functions preserving moments of three point masses must preserve moments of all measures. Our proofs exploit the semidefiniteness of the associated Hankel matrices and the complete monotonicity of the Laplace transforms of the underlying measures. As a byproduct, we …
Discrete Hankel Prolate Spheroidal Wave Functions: Spectral Analysis and Application
本文引入离散汉克尔长球面波函数（DHPSWF）作为离散多维能量最大化问题的径向解，推广Slepian经典工作，并给出其谱分析及对Ingham普适常数的上界估计。
In this paper we prove $L^p$ estimates for Stein's square functions associated to Fourier-Bessel expansions. Furthermore we prove transference results for square functions from Fourier-Bessel series to Hankel transforms. Actually, these are transference results for vector-valued multipliers from discrete to continuous in the Bessel setting. As a consequence, we deduce the sharpness of the range of $p$ for the $L^p$-boundedness of Fourier-Bessel Stein's square functions from the corresponding property for Hankel-Stein square functions. Finally, we deduce $L^p$ estimates for Fourier-Bessel multi…
The method of realizing certain self-reciprocal transforms as (absolute) scattering, previously presented in summarized form in the case of the Fourier cosine and sine transforms, is here applied to the self-reciprocal transform f(y)-> H(f)(x) = \int_0^\infty J_0(2\sqrt{xy})f(y) dy, which is isometrically equivalent to the Hankel transform of order zero and is related to the functional equations of the Dedekind zeta functions of imaginary quadratic fields. This also allows to re-prove and to extend theorems of de Branges and V. Rovnyak regarding square integrable functions which are self-or-sk…
By using a coset of closed subgroup, we define a Fourier like transform for locally compact abelian (LCA) topological groups. We studied two wavelet multipliers and Landau-Pollak-Slepian operators on locally compact abelian topological groups associated to the transform and show that the transforms are $L^p$bounded linear operators, and are in Schatten p-class for $1\leq p\leq \infty$. Finally, we determine their trace class and also obtain a connection with the generalized Landau-Pollak-Slepian operators.
We introduce two shearlet-based Ginzburg--Landau energies, based on the continuous and the discrete shearlet transform. The energies result from replacing the elastic energy term of a classical Ginzburg--Landau energy by the weighted $L^2$-norm of a shearlet transform. The asymptotic behaviour of sequences of these energies is analysed within the framework of $Γ$-convergence and the limit energy is identified. We show that the limit energy of a characteristic function is an anisotropic surface integral over the interfaces of that function. We demonstrate that the anisotropy of the limit energy…
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